If this thread interests you, you should check out "Blood Music" by Greg Bear. It's pretty old but the premise is that a researcher 'closes the loop' in a bunch of cells by making them able to edit their own DNA - thus making them Turing Complete.
Hilarity subsequently ensues.
Cells are already able to edit their own DNA. Examples include the yeast mating switch, in which the "active" gene is replaced by one of two templates, determining the role the yeast plays in mating (https://en.wikipedia.org/wiki/Mating_of_yeast#Mechanics_of_t...)
Further, your immune system does some clever combinatorial swapping to achieve diversity (https://en.wikipedia.org/wiki/V(D)J_recombination). The generated diversity is then screened by the immune system to find highly effective antibodies that bind to specific foreign invaders.
Doing something actually interesting from an engineering perspective makes for fun science fiction, but as always, the specific details in that story would be a very unlikely outcome.
As I get older, I'd be happy with some minor incremental progress on addressing myopia and hyperopia.